Past exam of the year 1 of the computer science course of the University of Oxford / 2013 / Discrete mathematics, probability and continuous mathematics / 8 / c / iii

The identity $XY=(S_1+S_2)(S_1-S_2)=S_1^2-S_2^2$ gives $\mathbb{E}[XY]=0$, since the two rolls have the same probability distribution. Also $\mathbb{E}[X]\mathbb{E}[Y]=7\cdot 0=0$. ThereforeThe two random variables are uncorrelated random variables, but that alone does not establish independence of random variables.